If a2=8, what are the first three terms of the sequence defined by the recursive formula below? an=3an-1+2

A8, 26, 80

B2, 8, 26

C8, 2, 0

D2, 8, 0

The answer is Letter B - 2, 8, 26

Given: an=3an-1+2; where a2=8

Required: First three terms of the sequence - a1, a2, a3

Solution:

You need to work back to get a1 since the given is a2.

To work back, minus 2 from 8 first before dividing the number by 3.

a1 = 8 - 2

a1 = 6 / 3

a1 = 2

In getting a3, multiply the given 8 by 3 then add 2. an=3an-1+2 : a3=3 (8) + 2

a3 = 8 x 3

a3 = 24 + 2

a3 = 26